代写MATH5965、代写R编程设计

日期：2023-02-19 10:44

Discrete Time Financial Modelling

Term 1, 2023

Cricos Provider Code: 00098G

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Staff

Position Name Email Room

Lecturer-in-charge Dr Donna Salopek dm.salopek@unsw.edu.au RC-1030

Please refer to your Timetable on MyUNSW for your Lecture/Seminar Tut, Lab enrolment days and

times. Timetable weblink: http://timetable.unsw.edu.au/2023/MATH5965.html

Administrative Contacts

Please visit the School of Mathematics and Statistics website for a range of information on School

Policies, Forms and Help for Students.

For information on Courses, please go to “Current Students” and either Undergraduate and/or

Postgraduate”, Course Homepage” for information on all course offerings,

The “Student Notice Board” can be located by going to the “Current Students” page; Notices are

posted regularly for your information here. Please familiarise yourself with the information found

in these locations. The School web page is: https://www.maths.unsw.edu.au

If you cannot find the answer to your queries on the web you are welcome to contact the Student

Services Office directly.

By email Postgraduate pg.mathsstats@unsw.edu.au

By phone: 9385 7053

Should we need to contact you, we will use your official UNSW email address of in the first

instance. It is your responsibility to regularly check your university email account. Please state

your student number in all emails.

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Course Information

We are aware some course exclusions on the Handbook may be different to the School website.

We are in the process of updating this information. Meanwhile, students should be following the

Handbook course information with the School website information as a supplement.

Course Aims

The course provides an overview of the most important classes of financial contracts that are

traded either on exchanges or over the counter between financial institutions and their clients. In

particular, options of European and American style, futures contracts and forward contracts are

discussed. We introduce the basic ideas of arbitrage pricing within the set-up of a one-period

model. In the next step, we analyse the valuation and hedging of European and American options

and general contingent claims in the framework of the classic Cox-Ross-Rubinstein binomial

model of the stock price. Finally, a general theory of arbitrage free discrete time models of spot

and futures markets is presented.

We prove the so-called Fundamental Theorems of Asset Pricing (FTAP) for a finite model of

security markets. The first FTAP establishes the equivalence between the no-arbitrage property of

a security market model and the existence of a martingale probability measure. The second FTAP

shows that the model completeness can be characterised in terms of the uniqueness of a

martingale probability measure.

Course Description

The course provides an overview of the most important classes of financial contracts that are

traded either on exchanges of over-the counter between financial institutions and their clients. We

discuss option of European and American style, futures contracts and forward contracts. The

basic ideas of arbitrage pricing are studied in the framework of the classical Cox-Ross-Rubinstein

binominal model of stock price.

Subsequently, we analyse the valuation and hedging of European and American options and

general contingent claims. We also prove the so-called fundamental theorems of asset pricing for

finite models of security markets which furnish a theoretical underpinning of the modern theory of

derivatives pricing in stochastic models of security markets.

Assessment and Deadlines

Assessment Week Weighting

%

Course Learning

Outcome (CLO)

Assignment 1: individual, Moodle Quiz Week 3 10% CLO2,

CL03

Assignment 2: Group work Week 7 15% ALL

Assignment 3: Group work Week 10 15% ALL

Final exam 60% ALL

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Late Submission of Assessment Tasks

A late penalty of 5% of the awarded mark will be applied per day or part day any assessment task

is submitted more than 1 hour late. (Where "late" in this context means after any extensions

granted for Special Consideration or Equitable Learning Provisions.) For example, an assessment

task that was awarded 75% would be given 65% if it was 1-2 days late. Any assessment task

submitted 7 or more days late will be given zero.

Note that the penalty does not apply to

Assessment tasks worth less than 5% of the total course mark, e.g. weekly quizzes,

weekly class participation, or weekly homework tasks.

Examinations and examination-style class tests

Pass/Fail Assessments

Course Learning Outcomes (CLO)

Recognise which analysis procedure is appropriate for a given research problem.

Apply probability theory and stochastic analysis to practical problems.

Understand the usefulness of probability and stochastic analysis in your professional area.

Course Schedule

The course will include material taken from some of the following topics. This is should only serve

as a guide as it is not an extensive list of the material to be covered and the timings are

approximate. The course content is ultimately defined by the material covered in lectures.

Weeks Topic Reading (if

applicable)

1 Introduction to Financial Derivatives and Probability

Refer to Moodle

Lecture notes

2 The Markov Property; Binomial Model Pricing and Hedging;

and Application to Exotic Options; Stopping Times and

American Options

3 State Prices and The Cox-Ross-Rubinstein Model

4 Security Markets in Discrete-Time

5 Random Walk; First Passage Times; Reflection Principle;

Perpetual American Options

7 Applications to pricing Barrier options and Lookback options

8 Special topic - TBA

9 Special topic - TBA

10 Special topic - TBA

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Suggested Textbooks

Steven E. Shreve: Stochastic Calculus for Finance I. The Binomial Asset

Pricing Model. Springer, 2004.

Stanley R. Pliska: Introduction to Mathematical Finance: Discrete Time Models.

Blackwell Publishers, Oxford, 1997.

Marek Musiela and Marek Rutkowski: Martingale Methods in Financial Modelling.

Springer-Verlag, Berlin Heidelberg New York, Second edition, 2005.

John C. Hull: Options, Futures, and Other Derivatives. Prentice-Hall, Englewood Cliffs,

1997.

Martin W. Baxter and Andrew Rennie: Financial Calculus. An Introduction to Derivative

Pricing. Cambridge University Press, Cambridge, 1997.

Hans Foellmer and Alexander Schied: Stochastic Finance: An Introduction in Discrete

Time. De Gruyter, 2000.

Nicholas Privault, Introduction to Stochastic Finances with Market Examples. Chapman and

Hall, 2022

Moodle

Log in to Moodle to find announcements, general information, notes, lecture slide, classroom tutorial

and assessments etc.

https://moodle.telt.unsw.edu.au

School and UNSW Policies

The School of Mathematics and Statistics has adopted a number of policies relating to enrolment,

attendance, assessment, plagiarism, cheating, special consideration etc. These are in addition to

the Policies of The University of New South Wales. Individual courses may also adopt other

policies in addition to or replacing some of the School ones. These will be clearly notified in the

Course Initial Handout and on the Course Home Pages on the Maths Stats web site.

Students in courses run by the School of Mathematics and Statistics should be aware of the School

and Course policies by reading the appropriate pages on the Maths Stats web site starting at:

https://www.maths.unsw.edu.au/currentstudents/assessment-policies

The School of Mathematics and Statistics will assume that all its students have read and

understood the School policies on the above pages and any individual course policies on the

Course Initial Handout and Course Home Page. Lack of knowledge about a policy will not be an

excuse for failing to follow the procedure in it.

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Academic Integrity and Plagiarism

UNSW has an ongoing commitment to fostering a culture of learning informed by academic

integrity. All UNSW staff and students have a responsibility to adhere to this principle of academic

integrity. Plagiarism undermines academic integrity and is not tolerated at UNSW. Plagiarism at

UNSW is defined as using the words or ideas of others and passing them off as your own.

The UNSW Student Code provides a framework for the standard of conduct expected of UNSW

students with respect to their academic integrity and behaviour. It outlines the primary

obligations of students and directs staff and students to the Code and related procedures.

In addition, it is important that students understand that it is not permissible to buy

essay/writing services from third parties as the use of such services constitutes plagiarism

because it involves using the words or ideas of others and passing them off as your own. Nor is

it permissible to sell copies of lecture or tutorial notes as students do not own the rights to this

intellectual property.

If a student breaches the Student Code with respect to academic integrity, the University may take

disciplinary action under the Student Misconduct Procedure.

The UNSW Student Code and the Student Misconduct Procedure can be found at:

https://student.unsw.edu.au/plagiarism

An online Module “Working with Academic Integrity” (https://student.unsw.edu.au/aim) is a six-

lesson interactive self-paced Moodle module exploring and explaining all of these terms and

placing them into your learning context. It will be the best one-hour investment you’ve ever made.

Plagiarism

Plagiarism is presenting another person's work or ideas as your own. Plagiarism is a serious

breach of ethics at UNSW and is not taken lightly. So how do you avoid it? A one-minute video for

an overview of how you can avoid plagiarism can be found

https://student.unsw.edu.au/plagiarism.

Additional Support

ELISE (Enabling Library and Information Skills for Everyone)

ELISE is designed to introduce new students to studying at UNSW.

Completing the ELISE tutorial and quiz will enable you to:

analyse topics, plan responses and organise research for academic writing and other

assessment tasks

effectively and efficiently find appropriate information sources and evaluate relevance

to your needs

use and manage information effectively to accomplish a specific purpose

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better manage your time

understand your rights and responsibilities as a student at UNSW

be aware of plagiarism, copyright, UNSW Student Code of Conduct and Acceptable Use of

UNSW ICT Resources Policy

be aware of the standards of behaviour expected of everyone in the UNSW community

locate services and information about UNSW and UNSW Library

Some of these areas will be familiar to you, others will be new. Gaining a solid understanding of all

the related aspects of ELISE will help you make the most of your studies at UNSW.

The ELISE training webpages:

https://subjectguides.library.unsw.edu.au/elise/aboutelise

Equitable Learning Services (ELS)

If you suffer from a chronic or ongoing illness that has, or is likely to, put you at a serious

disadvantage, then you should contact the Equitable Learning Services (previously known as

SEADU) who provide confidential support and advice.

They assist students:

living with disabilities

with long- or short-term health concerns and/or mental health issues

who are primary carers

from low SES backgrounds

of diverse genders, sexes and sexualities

from refugee and refugee-like backgrounds

from rural and remote backgrounds

who are the first in their family to undertake a bachelor-level degree.

Their web site is: https://student.unsw.edu.au/els/services

Equitable Learning Services (ELS) may determine that your condition requires special

arrangements for assessment tasks. Once the School has been notified of these, we will make

every effort to meet the arrangements specified by ELS.

Additionally, if you have suffered significant misadventure that affects your ability to complete the

course, please contact your Lecturer-in-charge in the first instance.

Academic Skills Support and the Learning Centre

The Learning Centre offers academic support programs to all students at UNSW Australia. We

assist students to develop approaches to learning that will enable them to succeed in their

academic study. For further information on these programs please go to:

http://www.lc.unsw.edu.au/services-programs

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Applications for Special Consideration for Missed Assessment

Please adhere to the Special Consideration Policy and Procedures provided on the web page below

when applying for special consideration.

https://student.unsw.edu.au/special-consideration

Please note that the application is not considered by the Course Authority, it is considered by a

centralised team of staff at the Nucleus Student Hub.

The School will contact you (via student email account) after special consideration has been

granted to reschedule your missed assessment, for a lab test or paper-based test only.

For applications for special consideration for assignment extensions, please note that the new

submission date and/or outcome will be communicated through the special consideration web site

only, no communication will be received from the School.

For Dates on Final Term Exams and Supplementary Exams please check the “Key Dates for Exams”

ahead of time to avoid booking holidays or work obligations.

https://student.unsw.edu.au/exam-dates

If you believe your application for Special Consideration has not been processed, you should email

specialconsideration@unsw.edu.au immediately for advice.

Course Evaluation and Development (MyExperience)

Student feedback is very important to continual course improvement. This is demonstrated within

the School of Mathematics and Statistics by the implementation of the UNSW online student

survey myExperience, which allows students to evaluate their learning experiences in an

anonymous way. myExperience survey reports are produced for each survey. They are released to

staff after all student assessment results are finalised and released to students. Course convenor

will use the feedback to make ongoing improvements to the course.